To answer these questions, we first extrapolate the gas production rate in our KB from the most recent extrasolar models. To do so, we compute the dust mass loss rate in the KB due to collisions using a state-of-the-art model of dust in our Solar System [1]}, [2]}. Indeed, according to extrasolar models that fit most observations to date [3]}, the gas production rate is proportional to the mass loss rate of the belt's collisional cascade, and we find (see Appendix ) that \(\sim 10^{-9}\)  M\(_\oplus \) /Myr of CO gas should be released in the current KB. The model's idea (which fits extrasolar observations) is that large planetesimals are composed of \(\sim \) 10% of CO [3]} that is released along with collisions that produce the observed dust (but the detailed physical mechanism is not constrained), either at the top (large km bodies) or further down the collisional cascade, but before solid bodies are ground down to dust and expelled by radiation pressure. We also use a more direct approach relying on the counting rate of the New Horizons dust counter to determine the dust production rate (rather than a numerical model) and arrive at the same value for the gas production rate. We also test a different more physically motivated model for releasing the CO and assume it comes from the slow heating provided by the Sun over long timescales, which warms up large bodies at greater depths as time goes by, and releases the CO in these increasingly deeper layers. We find that after 4.6 Gyr of evolution, only bodies larger than about 4 km can still contain CO (smaller bodies would have lost it already), and all together they release CO at a rate of \(\sim 2 \times 10^{-8}\)  M\(_\oplus \) /Myr. In this model, a single 30 km radius planetesimal would release around \(10^{-14}\)  M\(_\oplus \) /Myr, i.e., it is much lower than what can be detected with missions targeting specific KBOs [5]}. Fig. REF  shows the temporal evolution of the release rate, which goes down with time as only larger and larger bodies can participate as time goes by (see Appendix ). We note that this means that sampling the material in the KB now would not lead to the primordial volatile composition of planetesimals. We also test this slow stellar-driven heating model on more massive belts (similar to those observed around extrasolar systems) and show that it provides the right order of magnitude to explain CO observed around younger exo-systems, which may provide the first physical explanation for their ubiquitous CO presence.
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